Dark Light Higgs

We study a limit of the nearly-Peccei-Quinn-symmetric Next-to-Minimal Supersymmetric Standard Model possessing novel Higgs and dark matter (DM) properties. In this scenario, there naturally co-exist three light singlet-like particles: a scalar, a pseudoscalar, and a singlino-like DM candidate, all with masses of order 0.1-10 GeV. The decay of a Standard Model-like Higgs boson to pairs of the light scalars or pseudoscalars is generically suppressed, avoiding constraints from collider searches for these channels. For a certain parameter window annihilation into the light pseudoscalar and exchange of the light scalar with nucleons allow the singlino to achieve the correct relic density and a large direct detection cross section consistent with the CoGeNT and DAMA/LIBRA preferred region simultaneously. This parameter space is consistent with experimental constraints from LEP, the Tevatron, and Upsilon- and flavor physics.Comment: 4 pages, 4 figures, final version for Phys. Rev. Let

Structure preserving Stochastic Impulse Methods for stiff Langevin systems with a uniform global error of order 1 or 1/2 on position

Impulse methods are generalized to a family of integrators for Langevin systems with quadratic stiff potentials and arbitrary soft potentials. Uniform error bounds (independent from stiff parameters) are obtained on integrated positions allowing for coarse integration steps. The resulting integrators are explicit and structure preserving (quasi-symplectic for Langevin systems)

Space-time FLAVORS: finite difference, multisymlectic, and pseudospectral integrators for multiscale PDEs

We present a new class of integrators for stiff PDEs. These integrators are generalizations of FLow AVeraging integratORS (FLAVORS) for stiff ODEs and SDEs introduced in [Tao, Owhadi and Marsden 2010] with the following properties: (i) Multiscale: they are based on flow averaging and have a computational cost determined by mesoscopic steps in space and time instead of microscopic steps in space and time; (ii) Versatile: the method is based on averaging the flows of the given PDEs (which may have hidden slow and fast processes). This bypasses the need for identifying explicitly (or numerically) the slow variables or reduced effective PDEs; (iii) Nonintrusive: A pre-existing numerical scheme resolving the microscopic time scale can be used as a black box and easily turned into one of the integrators in this paper by turning the large coefficients on over a microscopic timescale and off during a mesoscopic timescale; (iv) Convergent over two scales: strongly over slow processes and in the sense of measures over fast ones; (v) Structure-preserving: for stiff Hamiltonian PDEs (possibly on manifolds), they can be made to be multi-symplectic, symmetry-preserving (symmetries are group actions that leave the system invariant) in all variables and variational

Temperature and Friction Accelerated Sampling of Boltzmann-Gibbs Distribution

This paper is concerned with tuning friction and temperature in Langevin dynamics for fast sampling from the canonical ensemble. We show that near-optimal acceleration is achieved by choosing friction so that the local quadratic approximation of the Hamiltonian is a critical damped oscillator. The system is also over-heated and cooled down to its final temperature. The performances of different cooling schedules are analyzed as functions of total simulation time.Comment: 15 pages, 6 figure

From efficient symplectic exponentiation of matrices to symplectic integration of high-dimensional Hamiltonian systems with slowly varying quadratic stiff potentials

We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for constant quadratic stiff potentials). This method is based on the highly-non-trivial introduction of two efficient symplectic schemes for exponentiations of matrices that only require O(n) matrix multiplications operations at each coarse time step for a preset small number n. The proposed integrator is shown to be (i) uniformly convergent on positions; (ii) symplectic in both slow and fast variables; (iii) well adapted to high dimensional systems. Our framework also provides a general method for iteratively exponentiating a slowly varying sequence of (possibly high dimensional) matrices in an efficient way

A new method for the determination of the locking range of oscillators

A time-domain method for the determination of the injection-locking range of oscillators is presented. The method involves three time dimensions: the first and the second are warped time scales used for the free-running frequency and the external excitation, respectively and the third is to account for slow transients to reach a steady-state regime. The locking range is determined by tuning the frequency of the external excitation until the oscillator locks. The locking condition is determined by analyzing the Jacobian matrix of the system. The method is advantageous in that the computational effort is independent of the presence of widely separated time constants in the oscillator. Numerical results for a Van Der Pol oscillator are presented

Improved transfer matrix method without numerical instability

A new improved transfer matrix method (TMM) is presented. It is shown that the method not only overcomes the numerical instability found in the original TMM, but also greatly improves the scalability of computation. The new improved TMM has no extra cost of computing time as the length of homogeneous scattering region becomes large. The comparison between the scattering matrix method(SMM) and our new TMM is given. It clearly shows that our new method is much faster than SMM.Comment: 5 pages,3 figure

Multi-photon Scattering Theory and Generalized Master Equations

We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time-evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S-matrix of the asymptotic in- and out- states. For the case of few incident photons in the waveguide, we also re-derive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the forth one, we show how a quantum emitter can generate entanglement of out-going photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.Comment: 21 pages,10 figure

Top Quark Pairs at High Invariant Mass - A Model-Independent Discriminator of New Physics at the LHC

We study top quark pair production to probe new physics at the LHC. We propose reconstruction methods for $t\bar{t}$ semileptonic events and use them to reconstruct the $t\bar{t}$ invariant mass. The angular distribution of top quarks in their c.m. frame can determine the spin and production subprocess for each new physics resonance. Forward-backward asymmetry and CP-odd variables can be constructed to further delineate the nature of new physics. We parametrize the new resonances with a few generic parameters and show high invariant mass top pair production may provide an early indicator for new physics beyond the Standard Model.Comment: 5 pages, 4 figures; version to appear in PR